Chapter 5 Section 5 Mathematics in Ming and Qing Dynasties——From Decline to Difficult Revival

After the middle of the Yuan Dynasty, Chinese mathematics declined sharply, and several works at the end of the Yuan Dynasty only improved the algorithm of multiplication and division.During the Yongle period of the Ming Dynasty (1403-1425 A.D.), the "Yongle Dadian" was compiled, and the previous Chinese mathematics works were transcribed according to their origin, various mathematical methods, sounds and meanings, and compilation categories.Most of the mathematical works of the Han, Tang, Song and Yuan Dynasties were scattered and lost in the Ming Dynasty. In the middle of the Qing Dynasty, Ye Xiu's "Siku Quanshu", the ancient Chinese calculation book mostly relied on it to be republished.

In the Ming Dynasty, stereotyped-legged scholars were selected, and their thoughts were severely imprisoned. Scholars seldom paid attention to mathematics.Gu Yingxiang and Tang Shunzhi were masters of mathematics in the Ming Dynasty, and they didn't understand Tianyuanshu and the method of multiplying and opening at all.In the first year of Jingtai (1450 A.D.), Wu Jing wrote ten volumes of "Nine Chapters Algorithm Comparison Encyclopedia", which collected application questions from past dynasties, and also abandoned the multiplication method and Tianyuan technique.After the Yuan and Ming Dynasties, with the completion of calculation and calculation algorithms, abacus calculations emerged and became popular, and a number of works on abacus calculations appeared in the Ming Dynasty.Its most author is Cheng Dawei's "Algorithm Tongzong" (AD 1592), with 17 volumes and 595 questions.This book meets the needs of business development, uses abacus calculation as the main calculation tool, and contains the method of abacus calculation.This book was reprinted and adapted many times in the next two or three hundred years, and its wide spread is rare.Cheng Dawei, courtesy name Rusi, nickname Qubin, was born in Xiuning (now Tunxi District, Huangshan City). He used to do business in the middle and lower reaches of the Yangtze River. He paid attention to collecting arithmetic and mathematics problems, and wrote this book in his later years.

At the end of the 16th century, European missionaries such as Matteo Ricci came to China and translated "Elements of Geometry" and other works together with Xu Guangqi and others.Later, the missionaries introduced western elementary mathematics such as trigonometry and logarithms. Since then, Chinese mathematics has begun the stage of being able to communicate with the West.Over the past 260 years of the Qing Dynasty, there have been many works on mathematics, all of which have integrated Chinese and Western mathematics to varying degrees. Mei Wending (AD 1633-1721) in Xuancheng of the Qing Dynasty devoted himself to the study of Chinese and Western mathematics and wrote many books. His grandson Mei Chengcheng edited his works into 60 volumes of "Mei Shi Series Collection", including 13 kinds of mathematical works and 40 volumes. It pervaded all categories of Chinese mathematics at that time, and had a great influence on mathematics in the Qing Dynasty.

Emperor Kangxi was fond of mathematics. He ordered 53 volumes of "The Essence of Mathematics and Physics" compiled by Mei Chengcheng, He Guozong, Ming Antu, Chen Houyao, etc., which comprehensively and systematically introduced the Western mathematical knowledge introduced at that time.The upper part is composed of five volumes, including the origin of mathematics and science, the original geometry, and the original arithmetic; the second part is divided into 40 volumes, including practical mathematics, ratio of borrowed root squares, logarithm, and trigonometric functions, etc., with 4 types of tables and 8 Juan also had a huge influence on Qing Dynasty mathematics.This book was printed in the first year of Yongzheng (AD 1723).

In 1723, Emperor Yongzheng came to the throne, thinking that the missionaries were not conducive to his rule, and drove all the missionaries to Macau except for a few who worked in the Qin Tianjian.Afterwards, the introduction of Western learning came to an end. Chinese mathematicians digested the previously introduced mathematical knowledge, and on the other hand were busy sorting out Chinese classical mathematics works. In 1773, Emperor Qianlong decided to revise the "Siku Quanshu", and Dai Zhen (AD 1724-1777) compiled "Zhoubi Suanjing", "Nine Chapters Suanshu", "Sea Island Suanjing", "Sunzi Suanjing" from "Yongle Dadian". Seven Sutras of the Han and Tang Dynasties, including Sutra of Five Cao Suanjing, Suanshu of Five Classics, and the counterfeit "Xiahouyang Suanjing", with collations, "Nine Chapters of Shu Shu", "Che Yuan Hai Jing", " The long-lost Song and Yuan calculation books such as "Siyuan Yujian" were also compiled or discovered one after another, which set off an upsurge in studying and sorting out Chinese classical mathematics during the Qianjia period (1736-1820 A.D.).The annotations of ancient books are greatly influenced by Li Huang's (?-1812 A.D.) "Nine Chapters of Fine Sketches of Arithmetic" and Luo Shilin's (1789-1853 A.D.) "Siyuan Yujian Fine Grass".The groundbreaking researches are based on Jiao Xun's (1763-1820 A.D.) "Li Tang Xue Suan Ji", Wang Lai (1768-1813 A.D.) "Hengzhai Suan Xue", Li Rui (1768-1817 A.D.) The most famous is "Suicide Notes on Mathematics".

At the beginning of the 18th century, the legal person Du Demei (1668-1720 A.D.) introduced the series expansion of the three trigonometric functions created by Newton and Gregory.Later, the study of trigonometric and logarithmic function expansions became an important topic for Chinese mathematicians.Ming Antu (late 17th century to 1860s), Dong Youcheng (AD 1791-1823), Xiang Mingda (AD 1789-1850), Dai Xu (AD 1805-1860) all made outstanding contributions.Li Shanlan (AD 1811-1882) made greater achievements in the research of trigonometric and logarithmic functions in "Fangyuan Explanation", "Argumentary Enlightenment", and "Logarithm Exploration" (AD 1845).The cone technique he created proposed several formulas equivalent to definite integrals, and independently approached calculus before contacting Western calculus ideas.Li Shanlan, courtesy name Renshu and nickname Qiuren, was born in Haining, Zhejiang.He was fond of mathematics in his childhood, and achieved creative achievements in his 30s.

In 1840, the big powers opened the closed door of the Qing Dynasty with cannons, and China gradually became a semi-feudal and semi-colonial society.Western mathematics was introduced in large quantities on an unprecedented scale. In 1852, Li Shanlan went to Shanghai and co-translated the last nine volumes of "Elements of Geometry", 13 volumes of "Algebra", and 18 volumes of "Ten Levels of Calculation" together with the British missionary William and Alex (AD 1815-1887). The latter is the first translation of calculus in China.Later, Hua Hengfang (AD 1833-1902) and the Englishman Fryer jointly translated books such as "Algebra", "Tracing the Origin of Microintegration", "Triangle Mathematics", and "Caussion Mathematics", the latter being the first in China. Probability theory translation.Many of the terms they coined are still in use today.Li Shanlan is also a master of Chinese and Western, and has written a lot. "Ellipse Zhengshu Solution" and other four are about the study of conic section, "Series Return" and so on are about the study of power series, and "Stack Product Ratio Class" systematically solves the high-order arithmetic difference on the basis of Zhu Shijie Series summation problem, and proposed the famous Li Shanlan identity. In 1872, he wrote "The Method of Checking the Roots of Numbers", which proved Fermat's little theorem and proposed the rule of determining prime numbers.His works are collected as "Zegu Xizhai Computing", including 14 scientific works.Li Shanlan is the first Chinese mathematician to carry out modern mathematics research.However, generally speaking, at the end of the Qing Dynasty, with economic decline and social turmoil, those who are interested in modern mathematics do not have the conditions to combine with modern engineering technology, and it is impossible to have a large number of considerable achievements. Because of my inherent prejudice in China, I don't ask for a deep understanding.Soon thereafter, especially after the Reformation and the New Culture Movement, the ancient Chinese mathematics tradition was basically interrupted, and Chinese mathematics research was incorporated into a unified modern mathematics. The 20th century is the century of Chinese mathematics renaissance, and people expect that China will regain its status as a great country in mathematics in the next century.